Show that for any two points A, B, you can still construct the segment between them.

Question

Suppose that our ruler is not a theoretical, Euclidean ruler, but instead has finite length. For concreteness, let’s say it’s 1 foot long. Let’s also suppose that our compass can “only” be opened 1 foot wide. Show that for any two points A, B, you can still construct the segment between them.



[Modified from Elementary Geometry from an Advanced Standpoint- (§19.1, # 7)

Answer 1

How long is the line to be drawn?

It would be easier to use a chalk-box (ball of string) then a straight-edge.

If the line is less than 2'; set the scale against point A towards point B.

Stick with the string.